On Steiner Versions of (bi)Connectivity in Network Problems

Abstract.

The notions of connectivity and biconnectivity can be generalized in the Steiner sense, i.e., they are restricted to a given subset of the vertices of a graph. We illustrate this generalization on two problems. The first problem is the bottleneck biconnected subgraph problem, the second one is the so-called bipartition problem. The adapted algorithms to solve the Steiner versions of these problems exploit depth-first search to attain respectively a running time of O(|E|+|V|log|V|) and O(|E|+|V|) with E denoting the set of edges and V the set of vertices of the given graph.